--- title: "5 Math Contest Preparation Strategies That Actually Work" description: "Five proven ways to prepare for the AMC 10/12, Waterloo contests and MATHCOUNTS: start with problems, practice weekly, cover core topics and manage time." url: https://bosenacademics.com/blog/math-contest-prep-strategies/ published: 2017-06-05T14:00:00Z updated: 2026-11-12T17:05:00Z section: "Math and computing contests" publisher: Bosen Academics (https://bosenacademics.com) --- # 5 Math Contest Preparation Strategies That Actually Work **The short answer:** Contest math rewards a different kind of thinking than school math. Start with problems instead of theory, practice 15 to 20 problems a week, cover number theory, combinatorics, geometry and algebra, train under timed conditions, and consider coaching to find gaps you can't see yourself. Math competitions such as the AMC 10/12, the Waterloo contests (Cayley, Fermat, Euclid) and MATHCOUNTS reward a style of mathematical thinking that ordinary classroom teaching doesn't always build. Students who excel at school math sometimes struggle in contests, not from lack of ability, but because contest math calls for different preparation. Here are five strategies that consistently produce results. ## 1. Where Should You Begin: Problems or Theory? Begin with problems. The most common mistake is studying contest math the way school math is studied: read the theory, then work practice problems. Contests run the other way. Try the problems first, wrestle with them, and only then learn the theory needed to crack them. This approach, often called problem-driven learning, develops the pattern recognition that separates good competitors from great ones. Start with past contest papers at the right level. For the AMC 10, work through problems 1 through 15 from recent years. For Waterloo contests, go through Cayley before attempting Euclid. Master the easier problems fully before moving up to harder ones. ## 2. How Many Problems Should You Do Each Week? Quality outweighs quantity, but volume still counts. During active preparation, aim for 15 to 20 problems a week, with at least 5 of them being ones you can't solve on the first try. The problems that defeat you are where the real learning happens. Keep a "problem journal" with full written solutions to every hard problem, including those you eventually had to look up. Go back through it each week. Students who regularly revisit their past struggles do better than those who only push on to new material. ## 3. Which Topics Deserve the Most Attention? Contest math draws heavily on a handful of core topics that school curricula tend to underplay: - **Number theory**: divisibility, modular arithmetic, prime factorization - **Combinatorics**: counting principles, probability, pigeonhole principle - **Geometry**: circle theorems, similar triangles, coordinate geometry tricks - **Algebra**: inequalities, sequences, functional equations A student who is comfortable in all four areas can make a real attempt at most of the problems on a typical AMC or Waterloo contest. ## 4. How Much Does Time Management Matter on Contest Day? A great deal. The AMC 10 allows 75 minutes for 25 problems, and the Euclid allows 2.5 hours for 10 multi-part problems. Plenty of students who know how to solve a problem still run out of time because they dwell too long on one question. Practice under timed conditions at least once a week. Learn to notice when you're stuck and move on, instead of grinding at one problem while easier points sit uncollected. A handy rule for the AMC: on the first pass, give no single problem more than 3 minutes. Once you've done everything you can solve quickly, go back to the ones you skipped. ## 5. Is a Tutor or Prep Course Worth It for Contest Math? Self-study with good problem books (such as "The Art and Craft of Problem Solving" or the AMC/AIME preparation volumes) can take a motivated student far. One-on-one coaching speeds things up considerably, though, because a skilled contest tutor can spot gaps in your problem-solving approach that you can't see yourself. A coach can also introduce elegant techniques and shortcuts that might take months to find alone. Related reading: - [Guide to the Euclid math contest](https://bosenacademics.com/blog/euclid-math-contest-guide/) - [IB math exam preparation](https://bosenacademics.com/blog/ib-math-aa-hl-exam-prep/) - [Tutoring approaches for gifted students](https://bosenacademics.com/blog/tutoring-gifted-advanced-students/) Contest math is among the most rewarding academic pursuits a student can take up. If your child is curious about competitive mathematics, [book a free consultation with Bosen Academics](https://bosenacademics.com/consultation/) to connect with an experienced contest math coach. ## Frequently asked questions ### What age should my child start contest math? Most students begin in grades 6 to 8 with MATHCOUNTS, the AMC 8 or the Waterloo Gauss contest. Starting in grade 9 or 10 is not too late, especially for students with strong foundational skills. ### Do math contest results help with university admissions? Yes, particularly for STEM programs. Strong results on the AMC/AIME, Euclid or national olympiads signal real mathematical talent, and a Euclid score in the top 25% or AMC qualification for AIME are meaningful achievements to list on applications. ### How long does it take to see improvement in contest scores? With 3 to 5 hours of consistent practice per week, most students improve noticeably within 3 to 4 months. Moving from the AMC 10 to AMC 12 level, or from Cayley to Euclid, typically takes 6 to 12 months of dedicated work. ### How much time should I spend on one problem during the AMC? On the first pass, no more than 3 minutes on any single problem. Skip what is stuck and come back after finishing everything you can solve quickly. ## Tutoring from Bosen Academics One-on-one tutoring from certified teachers and subject experts with master's and PhD degrees, in person in North York, Toronto, or online. Book a free consultation: https://bosenacademics.com/consultation/